*3.1. Local Thermal Cycle*

The thermal history at the site of interest during laser heating is a function of the processing parameters (Figure 9); depending on these, fusion may be experienced at the site of interest. The timescale is started at laser switch-on: since the process duration is dependent on the traveling speed, the time to get the peak temperature at the site of interest (i.e., to cover half the distance) is 5 s.

**Figure 9.** Thermal history of the site of interest as pyrometer output.

A recurring shape was found for the temperature profile: namely, a settling period, resulting in a leading thermal spike, was required by the device when entering the window of calibration (i.e., the operating range of acquisition); a trailing noise was found at the end of the acquisition, due to the air and argon overheating over the site of interest, instead. The thermal evolution shifted below or above the calibration limits under extreme conditions of processing, thus resulting in underflow or overflow, respectively.

For each processing condition, the thermal evolution of the site of interest was simulated (Figure 10) and compared with the acquisition. The peak temperature (*Tp*) acquired by the pyrometer focus was extracted and compared with the predicted peak temperature in order to quantitatively validate the thermal model (Table 3); the percentage difference between acquisition and simulation

was given. An agreement in a measure of 2.7%, absolute, on average, was found in terms of peak temperature; as regarding the conditions of underflow and overflow, the simulated thermal evolution was actually outside of the calibration window of the device.

**Figure 10.** Simulated thermal history of the site of interest for each processing condition.



### *3.2. Geometry of the Fusion Zone*

Since the overall size of the fusion zone depends on the thermal history, further information to validate the model was gathered upon inspections in a transverse cross-section with respect to the traveling direction of the laser beam (Figure 8). An indirect measurement of the simulated depth of the fusion zone had to be conducted: namely, a transverse plane at half-length was considered with respect to the traveling direction, then thermal contour lines are drawn (Figure 11). As expected, any increase in the experienced peak temperature yielded a proportional increase in the extent of the fusion zone.

**Figure 11.** Contour lines to define the extent of the fusion zone for each processing condition.

Based on the solidification range of the parent alloy, depth and width of the fusion zone were inferred. Indeed, since 775 K is the lower limit of the solidification range, fusion was experienced by any point above this temperature limit. For each given processing condition, the depth and width were compared to the corresponding actual geometry (Table 4). An agreement of 3.7% and 16.3%, absolute, on average, was found for depth and width, respectively. In order to improve the reliability of the model in predicting the width of the fusion zone, further investigation must be made and the dependence of the reflectivity on the starting roughness or oxide amount at the exposed surface should be considered.


**Table 4.** Depth and width of the fusion zone, actual vs. predicted.

#### **4. Conclusions**

A model to simulate laser heating was built and validated. The main elements were discussed and presented, aiming to offer a comprehensive description of the involved variables and phenomena. A super-Gaussian beam profile was implemented as an external thermal source; losses for radiation and convection were considered, whereas losses for plasma attenuation were neglected.

Under these assumptions, with an average error below 3%, the model is capable of predicting the peak temperature upon laser heating in a processing window ranging from 2 to 3 kW power and 4 to 6 mm/s speed, which is suitable to produce a melting pool where metal must be fed in additive manufacturing. With an average error below 4%, the model has been capable of predicting the depth of the fusion zone. Larger errors, of up to 16%, were found for the bead width instead; these will be addressed in future adjustments of the simulation; indeed, the dependence of the reflectivity on the starting roughness or oxide amount at the exposed surface should be considered. Furthermore, the model must be conveniently upgraded with powder or wire feeding to simulate layer-by-layer fabrication.

Interestingly, an industrial environment where a pyrometer output is used in real-time monitoring to match the intended thermal history, and, hence, the intended geometry, can be conceived. Nevertheless, proper actions both at software and hardware stages, must be taken to filter noise from the pyrometer output, depending on the system set-up, the metal to be processed, and the laser wavelength.

**Author Contributions:** Conceptualizationand Methodology, F.C.; Software, V.A.; Validation, Formal Analysis, Investigation, Data Curation, Writing-Original Draft Preparation, Writing-Review & Editing, F.C. and V.A.; Project Administration, F.C.

**Funding:** This research received no external funding.

**Acknowledgments:** The Authors gratefully acknowledge Eng. Antonio Criscitiello for his valuable support in programming the simulation tool.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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